Raman microscopy of a small uniaxial crystal: Tetragonal aspartame

A general method is presented for determining the shape and orientation of the Raman tensor of a molecule in a uniaxial crystal using a Raman microscope. First, equations are derived to connect the Raman tensor components (α_xx, α_yy, etc.) of a molecule to the Raman tensor components (α_aa, α_cc, etc.) of a crystal that is composed of molecules in a uniaxial arrangement, with an orientation specified by the two angles χ and θ. Next, a method is presented to obtain a correct set of values of the intensity ratios I_ac/I_aa and I_cc/I_aa from observed values of the intensity ratios measured with a Raman microscope. To augment the experimental data, the depolarization ratio ρ (for a completely random molecular orientation) is plotted as a function of r₁ = α_xx/α_zz and r₂ = α_yy/α_zz, so that a possible set of r₁ and r₂ values can be found from an observed value of ρ. The method has been applied to an aspartame IIA crystal (P4₁). A set of values of r₁, r₂, χ and θ has been determined for each of the following Raman fundamentals: 1741 cm⁻¹ (ester CO stretch), 1667 cm⁻¹ (amide I), 1275 cm⁻¹ (amide III) and 1204 cm⁻¹ (C C_phenyl stretch), excited at 488.0 nm.